What is the mean and variance of a random variable with the following probability density function?: #f(x) = 3x^2 if -1 < x < 1#; 0 otherwise
1 Answer
Nov 3, 2015
Mean
Explanation:
Note that
#E (X) = int_-1^1 x * (3x^2 ) " " dx#
# = int_-1^1 3x^3 " " dx#
# = 3 * [ x^4 /4 ]_( "(" - 1, 1 ")" )#
#=0#
Also note that
#"Var" (x) = E (X^2)- (E(X))^2#
# = 3 * [ x^5/5 ] _("("- 1, 1")") - 0^2 #
# = 3/5 * (1 + 1) #
#= 6/5#
